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World Displacement (Tessellation) not work correct when you have tiles, bricks, stones, pavements, grids, cells

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World Displacement (Tessellation) not work correct when you have grids and cells – tiles, bricks, stones, pavements, any rectangle draws as height map. Then only the horizontal and vertical middle grid line are calculated correct! Here is an complete example:

From the look of your model you do not have enough vertices to begin with on the plane to allow the tessellation and displacement to get the level of detail needed to produce the desired effect. If you look at the scene in wireframe you will see that there are not enough vertices in teh correct arrangement to allow for the smooth and crisp edges you are looking for. Tessellation does not simply add vertices and triangles in straight lines, it will sub divide your existing geometry based on factional factor algorithms. Here is another similar example of what I mean. In this first picture you can see I have the same tessellated and displaced material applied to each plane mesh. The Plane mesh on the left looks correct while the one on the right is jagged.

If you look at the same meshes in wireframe you can clearly see why, the tessellation although the same amount has produced far tighter results in a mesh that already had tight vertices.

Hopefully that helps explain why you are seeing these results. Balancing the number of vertices you bring in on the mesh with the amount generated through tessellation will give you far greater control over fine displaced details like the grid pattern.

Thanks Eric for your quick and detailed respond, but why material editor shows jagged plane or sphere (except the yellow cross on the middle) when current material is not connected to any plane or sphere or any shape yet? Any how to increase the vertices on my shape?

The Yellow Cross area that you are seeing that looks correct is based on the vertex layout of the sample assets in the viewport window. To increase vertices of the shape you will need to go into your 3D modeling program, and add edge loops to the model itself.